I. Basic Terms, Relations and Assumptions of the Theory of Elastic Orthotropic Shells. Some terms. General relationships of the theory of elastic orthotropic shells. Specific concepts of the theory of layered shells. Basic theory of sandwich shells. On possible formulations of simplified theories. Some limit processes. II. Membrane Theory of Layered Shells. Introductory remarks and working hypotheses. Cylindrical shells. Spherical shells. Conical shells. Thermoelastic membrane stresses. Applicability of the membrane theory. III. Axisymmetric Problems of the Bending Theory of Elastic Layered Cylindrical Shells. Introductory remarks and basic assumptions. Formulation and general solution of the problem. Limit processes for other types of fundamental systems. Derivatives of the members of fundamental systems. On the possibility of separating the membrane and bending states of stress. Generalized membrane state of stress. Boundary disturbances in long shells. Boundary disturbances in short shells. Thermoelastic stresses in shells with temperature dependent moduli E = E(T). IV. General Loading of Elastic Layered Cylindrical Shells. Introductory remarks and basic relations. Formulation of the problem. General solution of the problem. Axisymmetric part of the solution. Asymmetric part of the solution. Final solution for the given shell. V. Viscoelastic Structures. Introduction and notation. Hereditary theory. General formulation of the viscoelastic problem. On the possibility of separating variables. Elastic-viscoelastic analogy for homogeneous structures. Constructions of layered structure. VI. Complementary Chapters. Fourier series. Simple rheological materials (bodies). Schwartz distribution theory. References. Author Index. Subject Index.